\relax 
\citation{jackson:08}
\citation{goyal:07}
\citation{hummon00}
\citation{doreian06}
\citation{buskens-vanderijt:07}
\citation{goyal-vegaredondo:07}
\citation{kstw:08}
\citation{johnson:00}
\citation{anshelevich:03}
\citation{anshelevich:08}
\citation{fabrikant:03}
\citation{corbo:05}
\citation{galeotti:06}
\citation{jackson-wolinsky:96}
\citation{jackson:02}
\citation{myerson:91}
\citation{jackson-wolinsky:96}
\citation{jackson:08}
\citation{goyal:07}
\citation{hummon00}
\citation{doreian06}
\citation{goyal-vegaredondo:07}
\citation{johnson:00}
\citation{anshelevich:03}
\citation{anshelevich:08}
\citation{fabrikant:03}
\citation{corbo:05}
\citation{galeotti:06}
\citation{buskens-vanderijt:07}
\citation{kstw:08}
\citation{buskens-vanderijt:07}
\citation{kstw:08}
\citation{buskens-vanderijt:07}
\citation{kstw:08}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{\thepage }}
\newlabel{introduction}{{1}{\thepage }}
\citation{jackson-wolinsky:96}
\citation{aumann:88}
\citation{jackson:04}
\citation{jackson:08}
\citation{myerson:91}
\citation{myerson:91}
\citation{jackson:08}
\citation{goyal:07}
\citation{hummon00}
\citation{doreian06}
\citation{buskens-vanderijt:07}
\citation{goyal-vegaredondo:07}
\citation{kstw:08}
\citation{johnson:00}
\citation{anshelevich:03}
\citation{anshelevich:08}
\citation{fabrikant:03}
\citation{corbo:05}
\citation{galeotti:06}
\citation{jackson-wolinsky:96}
\citation{jackson:02}
\citation{jackson-wolinsky:96}
\citation{jackson-wolinsky:96}
\citation{hummon00}
\citation{jackson-wolinsky:96}
\citation{jackson-wolinsky:96}
\citation{hummon00}
\citation{jackson-wolinsky:96}
\citation{jackson-wolinsky:96}
\citation{doreian06}
\citation{fabrikant:03}
\citation{corbo:05}
\citation{corbo:05}
\citation{fabrikant:03}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Relevant Work}{\thepage }}
\newlabel{relevant-work}{{1.1}{\thepage }}
\citation{anshelevich:03}
\citation{anshelevich:08}
\citation{anshelevich:08}
\citation{goyal-vegaredondo:07}
\citation{goyal-vegaredondo:07}
\citation{buskens-vanderijt:07}
\citation{kstw:08}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Our Contributions}{\thepage }}
\newlabel{results}{{1.2}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Outline of The Paper}{\thepage }}
\newlabel{out-line}{{1.3}{\thepage }}
\@writefile{toc}{\contentsline {section}{\numberline {2}The Local Network Formation Game}{\thepage }}
\newlabel{utilitymodel}{{2}{\thepage }}
\citation{kstw:08}
\citation{jackson-wolinsky:96}
\citation{jackson:2003}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}The Strategic Form Game}{\thepage }}
\@writefile{lof}{\contentsline {figure}{\numberline {2.1}{\ignorespaces A stylized example }}{\thepage }}
\newlabel{model-illustration}{{2.1}{\thepage }}
\@writefile{toc}{\contentsline {section}{\numberline {3}Structure of Pairwise Stable \\Networks}{\thepage }}
\newlabel{sec:Stability}{{3}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Concept of Pairwise Stability}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Charactering pairwise-stable networks in LNFG}{\thepage }}
\newlabel{lem:StabilityConditions}{{1}{\thepage }}
\newlabel{lem:StabilityConditions1}{{2}{\thepage }}
\newlabel{eq:BaseUtility}{{3.1}{\thepage }}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1}{\ignorespaces $(a)$ After adding a new edge $ij$ $(b)$ After deleting edge $il$}}{\thepage }}
\newlabel{fig:complete-bipartite-network-abc}{{3.1}{\thepage }}
\newlabel{eq:UtilityAfterAddition}{{3.2}{\thepage }}
\newlabel{eq:ConditionForStabilityUnderAddition}{{3.3}{\thepage }}
\newlabel{eq:UtilityAfterDeletion}{{3.4}{\thepage }}
\newlabel{eq:ConditionForStabilityUnderDeletion}{{3.5}{\thepage }}
\newlabel{kpartite-result}{{3}{\thepage }}
\newlabel{additionedge}{{3.6}{\thepage }}
\newlabel{deletionedge}{{3.7}{\thepage }}
\newlabel{sigmai}{{3.8}{\thepage }}
\newlabel{simplify1}{{3.9}{\thepage }}
\newlabel{simplify2}{{3.10}{\thepage }}
\newlabel{deletionedge2}{{3.11}{\thepage }}
\citation{cplusplus}
\citation{boost}
\citation{hummon00}
\citation{hummon00}
\citation{hummon00}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces {\textbf  {Characterization of Network Structures \text  {under} the proposed utility Model}}}}{\thepage }}
\newlabel{summarytable2}{{1}{\thepage }}
\@writefile{toc}{\contentsline {section}{\numberline {4}Simulation Results}{\thepage }}
\newlabel{sec:Simulations}{{4}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Simulation Setup and Execution details}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Simulation Results}{\thepage }}
\citation{turan}
\citation{nor:ste}
\@writefile{lof}{\contentsline {figure}{\numberline {4.1}{\ignorespaces Regions of stability of some standard networks}}{\thepage }}
\newlabel{fig:Expected-Regions-of-stability}{{4.1}{\thepage }}
\@writefile{lof}{\contentsline {figure}{\numberline {4.2}{\ignorespaces Simulation Results for 10-actor networks}}{\thepage }}
\newlabel{fig:Simulation-Results-N=00003D10}{{4.2}{\thepage }}
\@writefile{toc}{\contentsline {section}{\numberline {5}Structure of Efficient Networks}{\thepage }}
\newlabel{sec:Efficiency}{{5}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Triangles in a Graph}{\thepage }}
\newlabel{turantheorem}{{5.1}{\thepage }}
\newlabel{theorem2}{{5.2}{\thepage }}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Finding the efficient graph}{\thepage }}
\newlabel{efficiency_equation}{{5.4}{\thepage }}
\newlabel{eqn5.5}{{5.5}{\thepage }}
\newlabel{eff_g_dash}{{5.6}{\thepage }}
\newlabel{deltagain}{{5.8}{\thepage }}
\newlabel{efficiency_equation1}{{5.9}{\thepage }}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces {\textbf  {Characterization of Efficient Network Structures in LNFG}}}}{\thepage }}
\newlabel{summarytable3}{{2}{\thepage }}
\newlabel{eff_g_dash1}{{5.10}{\thepage }}
\newlabel{conj1}{{1}{\thepage }}
\@writefile{toc}{\contentsline {section}{\numberline {6}Price of stability}{\thepage }}
\newlabel{POS}{{6}{\thepage }}
\bibcite{anshelevich:03}{1}
\bibcite{anshelevich:08}{2}
\bibcite{aumann:88}{3}
\bibcite{bala:00}{4}
\bibcite{buskens-vanderijt:07}{5}
\bibcite{corbo:05}{6}
\bibcite{doreian06}{7}
\bibcite{fabrikant:03}{8}
\bibcite{galeotti:06}{9}
\bibcite{goyal:07}{10}
\bibcite{goyal-vegaredondo:07}{11}
\bibcite{haller:03}{12}
\bibcite{hummon00}{13}
\bibcite{jackson-wolinsky:96}{14}
\bibcite{jackson:02}{15}
\bibcite{jackson:04}{16}
\bibcite{jackson:08}{17}
\bibcite{johnson:00}{18}
\bibcite{kstw:08}{19}
\bibcite{lopez:04}{20}
\bibcite{melendez:02}{21}
\bibcite{myerson:91}{22}
\bibcite{nor:ste}{23}
\bibcite{sarangi:03}{24}
\bibcite{jackson:2003}{25}
\@writefile{toc}{\contentsline {section}{\numberline {7}Conclusions and Future Work}{\thepage }}
\newlabel{conclusion}{{7}{\thepage }}
\@writefile{toc}{\contentsline {section}{\numberline {8}References}{\thepage }}
\bibcite{turan}{26}
\bibcite{boost}{27}
\bibcite{cplusplus}{28}
